On the stochastic nonlinear Schrödinger equation in dimension 2

Annie Millet (1, 2) , Zdzislaw Brzezniak (3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 University of York [York, UK]

We consider a non linear Schrödinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H1 under some general conditions on the diffusion coefficient. Under stronger conditions on the noise, the nonlinearity and the diffusion coefficient, we deduce the existence of a global solution when d = 2. This is a joint work with Z. Brzezniak.

Mots clés: nonlinear Schrödinger equation; Radonifying operators; Strotonovich integral; stochastic Strichartz inequality; compact manifolds; global existence

Domaines: Probabilités [math.PR]

Annie Millet, Zdzislaw Brzezniak. On the stochastic nonlinear Schrödinger equation in dimension 2. Women in Applied Mathematics, May 2011, Heraklion, Greece. http://www.acmac.uoc.gr/WAM2011/program.html. ⟨hal-00624578⟩